Find that value of k in the following quadratic equation whose roots are real and equal:
(k + 4) x² + (k + 1) x + 1 = 0

Question

Find that value of k in the following quadratic equation whose roots are real and equal:(k + 1)x2 – 2(k –1)x + 1 = 0

Philoid · Accepted Answer

When we compare the above quadratic equation with the generalized one we get,

ax² + bx + c = 0

a = k + 1

b = -2(k – 1)

c = 1

Since the quadratic equations have real and equal roots,

b² – 4ac = 0 for real and equal roots

⟹ (-2(k – 1)) ² – (4 × (k + 1) × 1) = 0

⟹ 4(k² - 2k + 1) – 4k - 4 = 0

⟹ 4k² - 8k + 4 – 4k - 4 = 0

⟹ 4k² - 12k = 0

⟹ 4k (k – 3) = 0

⟹ (k – 3) = 0 or 4k = 0

⟹ k = 3 or k = 0

Find that value of k in the following quadratic equation whose roots are real and equal:
(k + 1)x² – 2(k –1)x + 1 = 0